Solve (1/4)+4/5+2/5:(2/3)^3

$$( \frac { 1 } { 4 } ) + \frac { 4 } { 5 } + \frac { 2 } { 5 } : ( \frac { 2 } { 3 } ) ^ { 3 }$$

Evaluate

$$\frac{12}{5}=2.4$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{4}{5} to fractions with denominator 20.

$$\frac{5}{20}+\frac{16}{20}+\frac{\frac{2}{5}}{\left(\frac{2}{3}\right)^{3}}$$

Since \frac{5}{20} and \frac{16}{20} have the same denominator, add them by adding their numerators.

$$\frac{5+16}{20}+\frac{\frac{2}{5}}{\left(\frac{2}{3}\right)^{3}}$$

Add 5 and 16 to get 21.

$$\frac{21}{20}+\frac{\frac{2}{5}}{\left(\frac{2}{3}\right)^{3}}$$

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$\frac{21}{20}+\frac{\frac{2}{5}}{\frac{8}{27}}$$

Divide \frac{2}{5} by \frac{8}{27} by multiplying \frac{2}{5} by the reciprocal of \frac{8}{27}.

$$\frac{21}{20}+\frac{2}{5}\times \frac{27}{8}$$

Multiply \frac{2}{5} times \frac{27}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21}{20}+\frac{2\times 27}{5\times 8}$$

Do the multiplications in the fraction \frac{2\times 27}{5\times 8}.

$$\frac{21}{20}+\frac{54}{40}$$

Reduce the fraction \frac{54}{40} to lowest terms by extracting and canceling out 2.

$$\frac{21}{20}+\frac{27}{20}$$

Since \frac{21}{20} and \frac{27}{20} have the same denominator, add them by adding their numerators.

$$\frac{21+27}{20}$$

Add 21 and 27 to get 48.

$$\frac{48}{20}$$

Reduce the fraction \frac{48}{20} to lowest terms by extracting and canceling out 4.

$$\frac{12}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 3}{5} = 2\frac{2}{5} = 2.4$$